Identifying Best Interventions through Online Importance Sampling

TL;DR

This paper develops a novel bandit-based approach using online importance sampling to identify optimal interventions in causal graphs, with applications in biology and deep learning model interpretation.

Contribution

It introduces the first gap-dependent error and simple regret bounds for intervention selection using online importance sampling in causal graphs.

Findings

Outperforms existing methods on Flow Cytometry data

Effective in model interpretation of Inception-v3

Provides theoretical guarantees for intervention identification

Abstract

Motivated by applications in computational advertising and systems biology, we consider the problem of identifying the best out of several possible soft interventions at a source node $V$ in an acyclic causal directed graph, to maximize the expected value of a target node $Y$ (located downstream of $V$). Our setting imposes a fixed total budget for sampling under various interventions, along with cost constraints on different types of interventions. We pose this as a best arm identification bandit problem with $K$ arms where each arm is a soft intervention at $V,$ and leverage the information leakage among the arms to provide the first gap dependent error and simple regret bounds for this problem. Our results are a significant improvement over the traditional best arm identification results. We empirically show that our algorithms outperform the state of the art in the Flow Cytometry data-set, and also apply our algorithm for model interpretation of the Inception-v3 deep net that classifies images.